Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.AM.2

TRIG.28 Arc length and sector area Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.28 Arc length and sector area. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.28 Arc length and sector area - Primary standard selected for prompt fields in this prompt cell: UTRI.AM.2. Skill statement in this prompt cell: Determine arc length or sector area, or select the correct formula and substitution (using radians) for a given circle situation. Associated standards listed with this skill in this prompt cell: UTRI.AM.2; CCSS HSG.C.B.5; TEKS §111.41(c)(12)(B)-(C); FL MA.912.GR.6.4. Use this prompt-provided wording as the supporting standard description for this workflow.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Trigonometry

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related TRIG.28 Arc length and sector area skill assessments:

Problem 1Difficulty: Mastery
A sector has perimeter 40 units and area 75 square units. Which pairs of radius r and central angle theta are possible?
Ar = 5, theta = 6 only
Br = 15, theta = 2/3 only
Cr = 5, theta = 6 and r = 15, theta = 2/3
Dr = 10, theta = 2 and r = 20, theta = 1
Solution & Explanation:Perimeter gives r(2 + theta) = 40 and area gives 1/2 r2 theta = 75. The pairs r = 5, theta = 6 and r = 15, theta = 2/3 both satisfy both equations.
Problem 2Difficulty: Mastery
Two sectors have the same area. The first has radius 6 units and central angle 5 radians. The second has radius 10 units. What is the second sector's central angle?
Solution & Explanation:Equal areas mean 1/2(62)(5) = 1/2(102)theta. The first area is 90, so 90 = 50theta and theta = 1.8.
Problem 3Difficulty: Mastery
A bicycle wheel spoke is 14 inches long and turns through 2.25 radians. Which pair gives the rim arc length and swept sector area?
AArc length 31.5 inches, area 220.5 square inches
BArc length 31.5 inches, area 441 square inches
CArc length 16.25 inches, area 220.5 square inches
DArc length 28 inches, area 196 square inches
Solution & Explanation:Arc length is s = 14(2.25) = 31.5. Sector area is A = 1/2(142)(2.25) = 220.5.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this TRIG.28 Arc length and sector area worksheet?

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QIs this TRIG.28 Arc length and sector area worksheet free for teachers and homeschoolers?

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Trigonometry Math students. It aligns with educational standard UTRI.AM.2 (Primary standard selected for prompt fields in this prompt cell: UTRI.AM.2. Skill statement in this prompt cell: Determine arc length or sector area, or select the correct formula and substitution (using radians) for a given circle situation. Associated standards listed with this skill in this prompt cell: UTRI.AM.2; CCSS HSG.C.B.5; TEKS §111.41(c)(12)(B)-(C); FL MA.912.GR.6.4. Use this prompt-provided wording as the supporting standard description for this workflow.).

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